Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis

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dc.contributor.author Kirch, C en
dc.contributor.author Edwards, MC en
dc.contributor.author Meier, A en
dc.contributor.author Meyer, Renate en
dc.date.accessioned 2019-06-19T21:42:27Z en
dc.date.issued 2018 en
dc.identifier.citation Bayesian Analysis 37 pages 2018 en
dc.identifier.issn 1931-6690 en
dc.identifier.uri http://hdl.handle.net/2292/47253 en
dc.description.abstract Nonparametric Bayesian inference has seen a rapid growth over the last decade but only few nonparametric Bayesian approaches to time series analysis have been developed. Most existing approaches use Whittle’s likelihood for Bayesian modelling of the spectral density as the main nonparametric characteristic of stationary time series. It is known that the loss of efficiency using Whittle’s likelihood can be substantial. On the other hand, parametric methods are more powerful than nonparametric methods if the observed time series is close to the considered model class but fail if the model is misspecified. Therefore, we suggest a nonparametric correction of a parametric likelihood that takes advantage of the efficiency of parametric models while mitigating sensitivities through a nonparametric amendment. We use a nonparametric Bernstein polynomial prior on the spectral density with weights induced by a Dirichlet process and prove posterior consistency for Gaussian stationary time series. Bayesian posterior computations are implemented via an MH-within-Gibbs sampler and the performance of the nonparametrically corrected likelihood for Gaussian time series is illustrated in a simulation study and in three astronomy applications, including estimating the spectral density of gravitational wave data from the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO). en
dc.publisher International Society for Bayesian Analysis en
dc.relation.ispartofseries Bayesian Analysis en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.rights.uri https://creativecommons.org/licenses/by/4.0/ en
dc.subject stat.ME en
dc.subject stat.ME en
dc.subject 62M15, 62M10 en
dc.title Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis en
dc.type Journal Article en
dc.identifier.doi 10.1214/18-BA1126 en
dc.rights.holder Copyright: The authors en
pubs.author-url https://projecteuclid.org/euclid.ba/1540865702 en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Article en
pubs.elements-id 759863 en
pubs.org-id Science en
pubs.org-id Statistics en
pubs.arxiv-id 1701.04846 en
pubs.record-created-at-source-date 2019-08-15 en
pubs.online-publication-date 2018-10-30 en


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